Question

How do you solve $\left( {3x - 4} \right)\left( {3x - 5} \right)$?

Answer 1

Hint: We have multiplication of two polynomials that are $\left( {3x - 4} \right)$ and $\left( {3x - 5} \right)$. Both the polynomials have degree one and have two terms each. Hence, both polynomials are called binomials and linear polynomials. To multiply polynomials, first multiply each term in one polynomial by each term in the other polynomial using distributive law. Then, simplify the resulting polynomial by adding or subtracting the like terms.

Complete step-by-step answer:
Given, $\left( {3x - 4} \right)\left( {3x - 5} \right)$.
In the first polynomial, we have two terms and in the second polynomial also we have two terms. Multiply the first term of a polynomial with second polynomial and then the second term with second polynomial, we have,
$ \Rightarrow 3x\left( {3x - 5} \right) - 4\left( {3x - 5} \right)$
Opening the brackets and multiplying, we have,
$ \Rightarrow 9{x^2} - 15x - 12x + 20$
Adding the like terms, we have,
$ \Rightarrow 9{x^2} - 27x + 20$
Thus we have, $\left( {3x - 4} \right)\left( {3x - 5} \right) = 9{x^2} - 27x + 20$.
So, the correct answer is “$ 9{x^2} - 27x + 20$”.

Note: The degree of a polynomial is the highest of the degrees of the individual term with non-zero coefficients. We have different types of polynomials based on their degree such as constant polynomial, linear polynomial, quadratic polynomial, cubic polynomial, and quartic polynomial.